The math department recently purchased new learning software for their freshman math classes. The instructors want to use the learning software instead of a textbook. So they decide to study the effectiveness of the software. First they test the skills and concept mastery for a number of the freshman math students. Then they randomly divide the students into two groups. One group uses the learning software for a particular lesson and the other group uses the regular textbook. Then the instructors retest all of the students and compare the improvement in the skills and concept mastery for the two groups.what is the purpose of random assignment in this experiment?

The length of the diagonal AG = 7.56 cm.

A cuboid is a three-dimensional shape that is bounded by six rectangular faces. It is also known as a rectangular prism. A cuboid has six faces, twelve edges, and eight vertices.  

To find the Length of the side AG, find the length of AC by using the Pythagorean formula. Now using the trigonometric ratios formulas find the length of AG.

Here we have a cuboid

Where

AD = 23 cm

DC = 18 cm

∠GAC = 75°  

From the right angle triangle, ADC

=> AC² = AD² + DC²    [ Using the Pythagorean formula ]

=> AC² = (23)² + (18)²

=> AC² = 529 + 324

=> AC = √853 = 29.20    

From the right angle triangle, AGC

=> Cos B = AC/AG

=> Cos 75° = 29.20/AG

=> AG = Cos 75° (29.20)

=> AG = (0.26)(29.20)

=> AG = 7.56

Therefore

The length of the diagonal AG = 7.56 cm.

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The Venn Diagram for these given sets is graphed at the end of the answer.

A Venn Diagram uses circles to show if elements belong to one set, or multiple sets, in the intersection.

For this problem, we have that:

The Venn Diagram showing this is inserted at the end of the answer. There are a two erasers marks because of typing mistakes on my part.

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Answer:

Step-by-step explanation:

The expression that could be used to calculate the amount Trina was charged in interest for the billing cycle is  (APR / 365) x 30 days x adjusted balance.

The adjusted balance method is one of the methods for computing the finance charge (interest and other fees) for credit cards.

The adjusted balance is the ending balance determined after adjusting the opening balance with purchases and payments.

Credit card interest method = adjusted balance method

Beginning balance = $780

Purchase = $170

Payment = $210

Adjusted balance, AB = $740 ($780 + $170 - $210)

APR = 17% = 0.17 (17/100)

The interest charged = (APR / 365) x 30 days x adjusted balance

= $10.34 [(0.17/365) x 30 x $740]

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Answer:

ffffffffff

Step-by-step explanation:

fffffffffffffff

Answer:

Step-by-step explanation:

5). 3x + y = 5 -------(1)

    2x - y = 10 ---------(2)

    By adding equation (1) and (2),

    (3x + y) + (2x - y) = 5 + 10

    5x = 15

    x = 3

    From equation (1),

    3(3) + y = 5

    y = -4

6). 4x + 3y = 13 -------(1)

    x + y = 4 -------(2)

    Multiply equation (2) by 3 and subtract it from equation (1)

    (4x + 3y) - (3x + 3y) = 13 - 12

    x = 1

    From equation (2),

    1 + y = 4

    y = -3

7). x - 7y = 7 -----(1)

    -3x + 21y = -21

    -3(x - 7y) = -(3 × 7)

     x - 7y = 7 -------(2)

    Since, equation (1) and (2) are same, system of the equations will have infinitely many solutions.

8). x - 3y = 12

    3y = x - 12

    \(y=\frac{1}{3}x-4\) --------(1)

    3x - 9y = 18

    3(x - 3y) = 3(6)

    x - 3y = 6

    3y = x - 6

    \(y=\frac{1}{3}x-2\) ----------(2)

  Slopes of both the equations are same but the y-intercepts are different.

Therefore, both the lines are parallel and the system of equations will have no solution.

Step-by-step explanation:

Remember this trig identity?    sin^2 + cos^2 = 1

  (8/17)^2 + cos^2 = 1

     cos^2 = 1- 64/289 = 225/289

      cos = ± 15/17      since we are told it is in Q II   cos = - 15/17

tan = sin/ cos = 8/17 / -15/17 =  - 8/15

csc = 1/sin = 17/8

sec = 1/cos = - 17/15

cot = 1/tan = - 15/8

Answer:

10

2 multiplied by 15 is 30

15 x 2 = 30

Answer:

2 multiplied by. space is 30

Step-by-step explanation:

15 ×2 =30

Answer:

2 1/5 for alice

4 3/14 for Bert

5 for Carl

5 for Eva

5 1/2 for Dennis

Carl and Eva

Step-by-step explanation:

brainliest please

The length of the third side of the triangle is 8.

The image is that of a right angled triangle. A right angled triangle is a triangle in which one of the angles measure 90 degrees. The sum of angles in the triangle measure up to 180 degrees.

In order to determine the length of the third side, the Pythagoras theorem would be used.

The Pythagoras theorem: a² + b² = c²

where a = length

b = base

c = hypotenuse

In the triangle, 15 is the length and 17 is the hypotenuse.

a²  + 15²  = 17²

a²  = 17²  - 15²

a = √(17² - 15² )

a = √(289 -225)

√64 = 8

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Answer:

Find P percent of X

Find what percent of X is Y

Find X if P percent of it is Y

Step-by-step explanation:

Example: What is 10% of 150?

Convert the problem to an equation using the percentage formula: P% * X = Y

P is 10%, X is 150, so the equation is 10% * 150 = Y

Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10

Substitute 0.10 for 10% in the equation: 10% * 150 = Y becomes 0.10 * 150 = Y

Do the math: 0.10 * 150 = 15

Y = 15

So 10% of 150 is 15

Double check your answer with the original question: What is 10% of 150? Multiply 0.10 * 150 = 15

2

Answer:

it's being multiplied by 5 each number, if the pattern continues it would equal 0. But a zero exponent is 1 so it would be 5 as well because 5 x 1 is 5.

Step-by-step explanation

The pattern that can be noticed here is that each time the power of 5 is decreased by 1, the value of the resulting expression is divided by 5.

A number system is defined as a system of writing to express numbers.

The pattern that can be noticed here is that each time the power of 5 is decreased by 1, the value of the resulting expression is divided by 5.

As 5³ = 125, and then reduce the power of 5 by 1 to get 5², we can find the value by dividing 125 by 5, which gives us 25.

Similarly, to find the value of 5¹, we divide 25 by 5 to get 5.

If a is a positive number and n is a positive integer, then

aⁿ = (aⁿ⁻¹) x a

So, we can say that to find a power of a number when we know the value of a power that is either greater than or lesser than it by 1, we can multiply or divide the known value by a.

Hence, pattern that can be noticed here is that each time the power of 5 is decreased by 1, the value of the resulting expression is divided by 5.

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Answer: 45

Step-by-step explanation: 160-115= 45 you do this because the angles are across the vertex from each other.

Answer:

X=45

Step-by-step explanation:

Method 1 ( the long one)

So AED and CEB are vertical angles, that means that the are the same and have the same value.

So 115 plus x equal 160.

                            115 + x = 160

from there we just have to subtract 115 from both sides to get x by itself.

                            115 + x = 160

                           -115         -115

                       _________________

                                   x=45

Method 2 (short one

If you know that those are vertical angles, then just subtract 115 from 160 and there you go. You get 45.

Answer:

\(\boxed{\sf x = 80}\)

Step-by-step explanation:

A quadrilateral inscribed in a circle has opposite sides equal to 180.

So,

x + x + 20 = 180

2x + 20 = 180

Subtracting 20 from both sides

2x = 180 - 20

2x = 160

Dividing both sides by 2

x = 80

━━━━━━━☆☆━━━━━━━

▹ Answer

x = 80

▹ Step-by-Step Explanation

x + x + 20 = 180

2x + 20 = 180

2x = 180 - 20

2x = 160

x = 80

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

x=101

Step-by-step explanation:

Fun angles......................

Answer:

x = 79°

Step-by-step explanation:

The arrows on the line segments indicate that the lines are parallel.

As the parallel line segments are the same length, the other pair of opposite line segments are also parallel and the same length.  Therefore, we can apply the Alternate Interior Angles Theorem.

Alternate Interior Angles Theorem

If a line intersects a set of parallel lines in the same plane at two distinct points, the alternate interior angles that are formed are congruent.

Therefore, the missing angle in the triangle including angle x is 28°.

Interior angles of a triangle sum to 180°

⇒ 73° + 28° + x = 180°

⇒ x = 180° - 73° - 28°

⇒ x = 79°

(i) The first term (a) is 24 and the common difference (d) is -2.

(ii) The sum of the progression is 2520.

i) Finding the first term and common difference:

Given that the number of terms in the arithmetic progression is 40 and the last term is -54, we can use the formula for the nth term of an arithmetic progression to find the first term (a) and the common difference (d).

The nth term formula is: An = a + (n-1)d

Using the given information, we can substitute the values:

-54 = a + (40-1)d

-54 = a + 39d

We also know that the sum of the first 15 terms added to the sum of the first 30 terms is zero:

S15 + S30 = 0

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values for S15 and S30:

[(15/2)(2a + (15-1)d)] + [(30/2)(2a + (30-1)d)] = 0

Simplifying the equation:

15(2a + 14d) + 30(2a + 29d) = 0

30a + 210d + 60a + 870d = 0

90a + 1080d = 0

a + 12d = 0

a = -12d

Substituting this value into the equation -54 = a + 39d:

-54 = -12d + 39d

-54 = 27d

d = -2

Now we can find the value of a by substituting d = -2 into the equation a = -12d:

a = -12(-2)

a = 24

Therefore, the first term (a) is 24 and the common difference (d) is -2.

ii) Finding the sum of the progression:

The sum of the first n terms of an arithmetic progression can be calculated using the formula:

Sn = (n/2)(2a + (n-1)d)

Substituting the values:

S40 = (40/2)(2(24) + (40-1)(-2))

S40 = 20(48 - 39(-2))

S40 = 20(48 + 78)

S40 = 20(126)

S40 = 2520

Therefore, the sum of the arithmetic progression is 2520.

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The best estimate of how much she will spend on movies and eating out is given as follows:

$162.

The best estimate of how much she will spend on movies and eating out is obtained applying the proportions in the context of the problem.

The percentages associated with movies and eating out are given as follows:

The amount that she has left is given as follows:

$300.

Hence the best estimate of how much she will spend on movies and eating out is obtained as follows:

(0.3 + 0.24) x 300 = 0.54 x 300 = $162.

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For the given number 4 x 5³/₈. The whole part is 4 and the fraction part is 5³/₈. Both are added together to form a fraction of 43/8.

An inappropriate fraction can be created by converting a mixed fraction. Follow the instructions below to accomplish that.

For the given number 4 x 5³/₈.

The whole part is 4.

The fraction part is 5³/₈.

Solving the mixed fraction:

= 5³/₈.

= (5*8 + 3) /8

Both are added together to form a fraction:

= 43/8

The final number becomes:

= 4 x 5³/₈

= 4 x 43/8

= 43/2

Thus, the result of the final number obtained is 43/2.

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Answer:

Being that there are 195 countries, there would have to be 390 students

Step-by-step explanation:

The mechanical advantage of the given machine is 40, Velocity ratio is 80 and efficiency is 0.5.

The given question is concerned with finding the mechanical advantage, velocity ratio and efficiency of a weight lifting machine.

The problem has provided the following information:

Weight of the object, W = 1 kN = 1000 NEffort applied, E = 25 NHeight through which the object is lifted, h = 100 mm = 0.1 m Distance through which the effort is applied, d = 8 m

We know that, mechanical advantage = load/effort = W/E and velocity ratio = distance moved by effort/distance moved by the load.Mechanical advantage

The mechanical advantage of the given machine is given by; Mechanical advantage = load/effort = W/E= 1000/25= 40Velocity ratioThe velocity ratio of the given machine is given by;

Velocity ratio = distance moved by effort/distance moved by the load.= d/h = 8/0.1= 80EfficiencyThe efficiency of the given machine is given by;

Efficiency = (load × distance moved by load) / (effort × distance moved by effort)Efficiency = (W × h) / (E × d)= (1000 × 0.1) / (25 × 8)= 0.5

Therefore, the mechanical advantage of the given machine is 40, velocity ratio is 80 and efficiency is 0.5.

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The length of the diagonal of a square with a perimeter of 56 is 14√2.

A diagonal is the longest line that divides a plane shape into two equal parts.

To calculate the length of the diagonal of the square, first we need to find the length of the square using the perimeter formula.

Formula:

Where:

From the question,

Given:

Substitute the value into equation 1 and solve for a

Finally to find the length of the diagonal of the square, we use the formula below

Where:

Substitute into equation 2

Hence, the length of the diagonal is 14√2.

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Answer:

qfewwqeffwqfefewqwqreg

Step-by-step explanation:

Answer:

1. 7

2. 35

3 & 4. 7x = 70

5. 10

Step-by-step explanation:

Using sampling concepts, it is found that:

a) The population of interest is all bank institutions in the region that are Implementing mobile app relationship management solution.

b) The sample is given by the 155 executives representing bank institutions.

c) The possible parameter of interest is the proportion of bank institutions in the region that cite mobile app banking enhancements as the greatest anticipated strategy.

d) The statistic used to estimate the parameter is: 36% of executives representing bank institutions in the study cite mobile app banking enhancements as the greatest anticipated strategy.

Hence, for this problem:

a) The population of interest is all bank institutions in the region that are Implementing mobile app relationship management solution.

b) The sample is given by the 155 executives representing bank institutions.

Hence:

c) The possible parameter of interest is the proportion of bank institutions in the region that cite mobile app banking enhancements as the greatest anticipated strategy.

From the sample, the percentage is of 36%, hence:

d) The statistic used to estimate the parameter is: 36% of executives representing bank institutions in the study cite mobile app banking enhancements as the greatest anticipated strategy.

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Looks like the integral should be

\(\displaystyle\int\frac{x+2}{\sqrt{x+(2x+3)^2}}\,\mathrm dx\)

Expand the denominator:

\(\displaystyle\int\frac{x+2}{\sqrt{4x^2+13x+9}}\,\mathrm dx\)

Notice that

\(u=4x^2+13x+9\implies \mathrm du=(8x+13)\,\mathrm dx\)

In order to use this substitution, expand the integral as

\(\displaystyle\frac18\int\frac{8x+13}{\sqrt{4x^2+13x+9}}\,\mathrm dx+\frac38\int\frac{\mathrm dx}{\sqrt{4x^2+13x+9}}\)

In the first integral, use the previously mentioned substitution:

\(\displaystyle\frac18\int\frac{8x+13}{\sqrt{4x^2+13x+9}}\,\mathrm dx=\frac18\int\frac{\mathrm du}{\sqrt u}=\frac14\sqrt u\)

\(=\dfrac14\sqrt{4x^2+13x+9}\)

In the second integral, complete the square in the denominator:

\(4x^2+13x+9=4\left(x+\dfrac{13}8\right)^2-\dfrac{25}{16}\)

Now substitute

\(x=\dfrac58\sec t-\dfrac{13}8\implies\mathrm dx=\dfrac58\sec t\tan t\,\mathrm dt\)

so that

\(\sec t=\dfrac{8x+13}5\)

Then

\(4x^2+13x+9=\dfrac{25}{16}(\sec^2t-1)=\dfrac{25}{16}\tan^2t\)

and the integral becomes

\(\displaystyle\frac{\frac{15}{64}}{\frac54}\int\frac{\sec t\tan t}{\sqrt{\tan^2t}}\,\mathrm dt=\frac3{16}\int\sec t\,\mathrm dt\)

\(=\dfrac3{16}\ln|\sec t+\tan t|\)

\(=\dfrac3{16}\ln\left|\dfrac{8x+13}5+\dfrac{\sqrt{(8x+13)^2-25}}5\right|\)

So, the integral is

\(\dfrac14\sqrt{4x^2+13x+9}+\dfrac3{16}\ln\left|\dfrac{8x+13}5+\dfrac{\sqrt{(8x+13)^2-25}}5\right|+C\)

Answer:

41.81 ; 12.67

Step-by-step explanation:

Given the data:

Age range, years 18-28 29-39 40-50 51-61 62 and over

Midpoint x 23 34 45 56 67

Percent of super shoppers 9% 46% 22% 11% 12%

Midpoint, x : 23 34 45 56 67

Frequency, f : 0.09_ 0.46 _ 0.22 __0.11 __ 0.12

The mean(m)

Σfx / Σf

[(23 * 0.09) + (34 * 0.46) + (45 * 0.22) + (56 * 0.11) + (67 * 0.12)] / (0.09 + 0.46 + 0.22 + 0.11 + 0.12)

= 41.81 / 1

Mean = 41.81

Standard deviation :

Sqrt[(Σ(X² * f) / Σf) - m²)]

((23^2*0.09) + (34^2*0.46) + (45^2*0.22) + (56^2*0.11) + (67^2*0.12)) / 1

1908.51 - 41.81^2

Sqrt(160.4339)

= 12.666250

= 12.67

The height of the building can be  649.44 ft

What is angle of elevation ?

angle of elevation states that the angle which is formed between line of sight and horizontal line.

Given,  the base of the triangle is 1.75 mile. The angle opposite of the tall side, x, is 4 degrees.

height of the building is an unknown variable (x) .

tan(angle) = opposite length /adjacent length.

Opposite length is x, adjacent length is 1.75 mile, angle is 4 degrees.

tan(4º) = x / 1.75

rearrange for x

x = 1.75*tan(4º) = ~1.75*0.0699  miles.

x = ~0.123

Now to get feet, just multiply by 5,280 ft in one mile

Height of the building is 0.123 miles * 5280 ft/mile = 649.44 ft

Hence , The height of the building can be  649.44 ft .

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